Sorry to hear your woes with FAC, Garden shootings not too different in a way to shooting on a perm.
You must have the Landowners permission if you do not own the Property.
All Ammunition must remain within the property boundry and reasonable means to keep it that way, i.e good backstop etc.
You must not shoot in a way to cause impedance to a road user or prove possible risk withing 50m of a roadway (simply avoid shooting towards roads/footpaths and if you must make sure nothing can get through, again good backstop)
Noise wise its pretty much the same as anything, do your best to keep it down but as long as it's within acceptable levels and sociable hours all should be good.
If you want to hunt something it's pretty much small game only for sub12, species you will need to check if it is acceptable to shoot as some birds are protected as are things like red squirrels but your common all garden feral pigeon, rats and grey squirrels are all fair game and being already a hunter you'll know about appropiate shots etc.
Part of the fun I've found with my Garden shooting is being able to build and experiment with my own targets, plinking has so many options you won't find yourself missing the extra power.